A Modal Logic for Subject-Oriented Spatial Reasoning

Authors Przemysław Andrzej Wałęga, Michał Zawidzki

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Przemysław Andrzej Wałęga
  • University of Oxford, Department of Computer Science, United Kingdom
  • University of Warsaw, Institute of Philosophy, Poland
Michał Zawidzki
  • University of Łódź, Department of Logic, Poland

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Przemysław Andrzej Wałęga and Michał Zawidzki. A Modal Logic for Subject-Oriented Spatial Reasoning. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We present a modal logic for representing and reasoning about space seen from the subject’s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Verification by model checking
  • spatial logic
  • modal logic
  • subject-oriented
  • computational complexity


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